Operations Research (IN0024)

Prof. Dr. Martin Bichler

Dr. Halil Bayrak · Janik Bürgermeister · Teodora Dobos · Dr. Abheek Ghosh · Jan Höhener

Description

The lecture introduces optimization methods with a focus on linear and integer linear optimization, network flow problems, and nonlinear optimization. The course provides weekly exercises. A solid understanding of linear algebra and analysis is a prerequisite.

As in the last years, this course will not be streamed or recorded, but there is a comprehensive set of lecture slides and exercises provided on Moodle.

Lecture Schedule

• 13.04 Introduction, Tutorials Organization
• 16.04 Modeling with Linear Programming
• 20.04 Solving Linear Programs, Convexity
• 23.04 Simplex Algorithm
• 27.04 Revised Simplex Algorithm in Matrix Notation
• 30.04 Sensitivity Analysis
• 18.05 Duality Theory, Min-Max Theorem
• 28.05 Modeling Integer Problems
• 01.06 Solving Integer Problems
• 08.06 Column Generation, Approximation Algorithms
• 11.06 Polynomial-Time Solvable Integer Problems: Total Unimodularity, Matroids
• 18.06 Network Flow Problems
• 22.06 Traveling Salesperson Problem
• 25.06 Nonlinear Optimization
• 29.06 Convex Optimization
• 02.07 Online Convex Optimization

Organization

• Moodle course: https://www.moodle.tum.de
• Teaching materials:
  • The slide deck corresponding to the lecture will be available on Moodle after the lecture. A textbook (see recommendations below) is essential for the course!
• Place and time:
  • Monday and Thursday, 12:10, Interims II, Hörsaal 2; no live streaming
• Registration: Registration for the lecture via TUMonline is required to receive access to the teaching materials on Moodle.
• Exams:
  • Midterm exam (60min) 12.05 08:00-09:00
    Registration via TUMonline: 20.04 - 04.05
  • Endterm exam (120min) 07.08 17:00-19:00
    Registration via TUMonline: To be announced
  • Retake exam (120min) 29.09 08:00-10:00
    Registration via TUMonline: To be announced

Tutorials

Two types of tutorials are offered:

• Central exercise - Friday 16:15 - 17:45, MI HS 1
  In the central exercise, a teaching assistant discusses solutions to typical problems with students. The central exercise is streamed via TUM-Live.
• Tutor groups - 8 groups, Tuesday - Friday, MI 01.010.011
  An exercise sheet is published weekly on Moodle. Students solve the sheet in the tutor groups. Suggested solutions are discussed together with a student tutor and then published on Moodle.

Exam & Grade Bonus

• There will be two exam opportunities (endterm and retake). Both exams are planned as on-site exams. There will be no online exam option.
• A non-programmable calculator is allowed for the exam.
• In addition to registering for the lecture and tutorials, you must also register for the exam if you wish to take it.
• A midterm exam is also offered, which allows you to earn a grade bonus (0.3 grade points). The grade bonus will be included to the exam grade only if you passed the exam.
• The grade bonus is also valid for the retake exam in the summer semester 2026, but cannot be transferred to future semesters.

Literature

• Winston, A.: Operations Research, Algorithms and Applications, Wiley & Sons, Duxbury Press, 2003. (Available in the library.)
• Koop, A.; Moock, H.: Lineare Optimierung – eine anwendungsorientierte Einführung in Operations Research, Springer, 2018.
• Vanderbei, R.: Linear Programming, 3rd edition, ISOR, 2008.
• Bertsimas, D.; Tsitsiklis, J.: Introduction to Linear Optimization, Athena Scientific, 1997.

• Nemhauser, G.; Wolsey, L.: Integer and Combinatorial Optimization, Wiley-Interscience, 1999.